Coarsening in the two-dimensional soap froth and the large-Q Potts model: A detailed comparison

Abstract A detailed comparison between the experimental evolution of a two-dimensional soap froth and a next-nearest-neighbour Q = ∞ Potts model on a square lattice starting from identical initial conditions is presented. We compare the pattern evolution, dynamics, distribution functions and correlations of the two systems. We also examine in detail the relation between number or sides and area (Lewis' law) and two measures of pattern disorder. Overall agreement is found between the model and simulation, with a few systematic deviations which suggest that side redistribution is affected by subtle anisotropy and equilibration effects.

[1]  Glazier,et al.  Nonideal effects in the two-dimensional soap froth. , 1989, Physical review. A, General physics.

[2]  K. Kawasaki,et al.  Scaling behavior of two-dimensional domain growth: Computer simulation of vertex models , 1989 .

[3]  Katsuya Nakashima,et al.  Vertex models for two-dimensional grain growth , 1989 .

[4]  Glazier,et al.  Soap froth revisited: Dynamic scaling in the two-dimensional froth. , 1989, Physical review letters.

[5]  David J. Srolovitz,et al.  Computer simulation of normal grain growth in three dimensions , 1989 .

[6]  Carl V. Thompson,et al.  Computer simulation of microstructural evolution in thin films , 1988 .

[7]  J. Iglesias,et al.  Towards statistical mechanics of a 2D random cellular structure , 1988 .

[8]  K. Kawasaki,et al.  Statistical theory of Ostwald ripening with elastic field interaction , 1988 .

[9]  H. Atkinson Overview no. 65 , 1988 .

[10]  Marder Soap-bubble growth. , 1987, Physical review. A, General physics.

[11]  Gross,et al.  Dynamics of two-dimensional soap froths. , 1987, Physical review. A, General physics.

[12]  Beenakker Evolution of two-dimensional soap-film networks. , 1986, Physical review letters.

[13]  A. C. Ferro,et al.  Computer simulation of grain growth in a bidimensional polycrystal , 1985 .

[14]  David J. Srolovitz,et al.  Computer simulation of grain growth—V. Abnormal grain growth , 1985 .

[15]  A. S. Kravchenko,et al.  Experimental investigation of normal grain growth in terms of area and topological class , 1985 .

[16]  L. Shvindlerman,et al.  Computer simulation of grain growth in two dimensions , 1985 .

[17]  Michael P. Anderson,et al.  Computer simulation of grain growth—IV. Anisotropic grain boundary energies , 1985 .

[18]  P. S. Sahni,et al.  Computer simulation of grain growth—I. Kinetics , 1984 .

[19]  P. S. Sahni,et al.  Computer simulation of grain growth—II. Grain size distribution, topology, and local dynamics , 1984 .

[20]  D. Weaire,et al.  The evolution of the structure of a two-dimensional soap froth , 1983 .

[21]  P. S. Sahni,et al.  Grain growth in two dimensions , 1983 .

[22]  Denis Weaire,et al.  Theory of the arrangement of cells in a network , 1981 .

[23]  A. Mocellin,et al.  Grain coordination in plane sections of polycrystals , 1979 .

[24]  Denis Weaire,et al.  Some remarks on the arrangement of grains in a polycrystal , 1974 .

[25]  D. A Aboav,et al.  The arrangement of grains in a polycrystal , 1970 .

[26]  W. Mullins Two‐Dimensional Motion of Idealized Grain Boundaries , 1956 .

[27]  R. Kikuchi Shape Distribution of Two‐Dimensional Soap Froths , 1956 .

[28]  P. Beck Annealing of cold worked metals , 1954 .

[29]  F. T. Lewis,et al.  The correlation between cell division and the shapes and sizes of prismatic cells in the epidermis of cucumis , 1928 .

[30]  K. Kawasaki,et al.  Two-dimensional vertex model with local friction coefficient , 1989 .

[31]  C. V. Thompson,et al.  A two-dimensional computer simulation of capillarity-driven grain growth: Preliminary results , 1988 .

[32]  Denis Weaire,et al.  Monte Carlo simulation of the evolution of a two-dimensional soap froth , 1986 .

[33]  N. Hansen,et al.  Annealing Processes - Recovery, Recrystallization and Grain Growth: Proceedings of the 7. Risø International Symposium on Metallurgy and Materials Science, Risø, 8-12 September 1986 , 1986 .

[34]  N. Rivier On the structure of random tissues or froths, and their evolution , 1983 .

[35]  Ian K. Crain,et al.  The Monte-Carlo generation of random polygons , 1978 .

[36]  C. Lantuéjoul Computation of the Histograms of the Number of Edges and Neighbours of Cells in a Tessellation , 1978 .

[37]  R. E. Miles,et al.  Geometrical probability and biological structures, Buffon's 200th anniversary : proceedings of the Buffon Bicentenary Symposium on Geometrical Probability, Image Analysis, Mathematical Stereology, and Their Relevance to the Determination of Biological Structures, held in Paris, June 1977 , 1978 .